Decide whether 301 is term of given sequence 5, 11, 17, 23, ..... Activity :- Here, d = □, therefore this sequence is an A.P. a = 5, d = □ Let nth term of this A.P. be 301 tn = a + (n – 1) □ 301 - Algebra

Sum

Decide whether 301 is term of given sequence 5, 11, 17, 23, .....

Activity :-  Here, d = square, therefore this sequence is an A.P.

a = 5, d = square

Let nth term of this A.P. be 301

tn = a + (n – 1) square

301 = 5 + (n – 1) × square

301 = 6n – 1

n = 302/6 = square

But n is not positive integer.

Therefore, 301 is square the term of sequence 5, 11, 17, 23, ......

Solution

Here, d = 11 – 5 = 6, therefore this sequence is an A.P.

a = 5, d = 6

Let nth term of this A.P. be 301

tn = a + (n – 1) d

∴ 301 = 5 + (n – 1) × 6

∴ 301 = 5 + 6n – 6

∴ 301 = 6n – 1

∴ 6n = 302

∴ n = 302/6 = 151/3

But n is not positive integer.

Therefore, 301 is not the term of sequence 5, 11, 17, 23, ......

Concept: General Term of an Arithmetic Progression
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